I am not sure if the concern is using "wrong" suppliers or, more likely, obscure devices. If you stick with the mainstream parts made by multiple companies ("dual sourced"), then you will usually not have a problem. If you are concerned, call the supplier and ask to talk to the Product Manager of what ever product line you need information on (e.g microcontrollers, amplifiers, discrete transistors, ...). Then simply ask if this part is scheduled for deletion. It is probably not necessary to ask unless the DATASHEET has not been updated within the past five years or if inventory at distributors (usually posted) appears to be unnaturally small. The one category that seems to have a very short life cycle lately is high power LEDs. Cree, Osram, Philips-lumiled, Epistar and Toshiba are the majors and they seem to have lifetimes of 18 months or less. The smaller suppliers are worse, they seem to make one campaign and off to the next highest power LED next week.

Sorry, I chose this list specifically to show that even big companies come and go.
These have all been taken over by other companies, the most notable one, of course, is National Semiconductor which has be absorbed into Texas Instruments.

Motorola chips are now manufactured by either ON or Freescale.

There are some very useful chips that have been produced in the past by big name companies that are now obsolete or difficult to find.